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Vector-Valued Entire Functions of Bounded Index Satisfying a Differential Equation
Abstract:
The concept of complex valued entire functions of hounded index is extended to C -valued entire functions by replacing the absolute value in the definition of an entire function of bounded index by the maximum of the absolute values of the components. If the components of a C -valued entire function are of bounded index, then the function is also of bounded index; however a C -valued function may be of bounded index without all of its components being of bounded index. Solutions of certain linear differential equations are related to C -valued functions of bounded index.
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